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Proof step 2 from proof range-put (previous step)

n < nused, nused ≤ # zbrar, nused ≠ 0 → key ≤ zbrar[n].key, n ≠ 0 → zbrar[n - 1].key < key ⊦ key-range(zbrar, n, nused, ri[key, adr]) = key-range(zbrar, n, nused, ri)[key, adr]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < nused, n < # zbrar, nused ≤ # zbrar, n ≠ 0 → zbrar[n - 1].key < key ⊦ key-range(zbrar, n, nused, ri[key, adr]) = key-range(zbrar, n, nused, ri)[key, adr], zbrar[n].key < key

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ key0 ≤ key1 ↔ ¬ key1 < key0; (s)% ⊦ m < n → n ≠ 0; (s)